3.2.1.1 First

glm1 <- glmer(fec ~ age + (1| id),data=cham2, family = binomial)
summary(glm1)

## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: binomial  ( logit )
## Formula: fec ~ age + (1 | id)
##    Data: cham2
## 
##      AIC      BIC   logLik deviance df.resid 
##   1775.1   1790.7   -884.6   1769.1     1325 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -1.6411 -1.1386  0.6819  0.7903  1.0477 
## 
## Random effects:
##  Groups Name        Variance Std.Dev.
##  id     (Intercept) 0.2129   0.4614  
## Number of obs: 1328, groups:  id, 217
## 
## Fixed effects:
##             Estimate Std. Error z value Pr(>|z|)    
## (Intercept)  0.58024    0.15766   3.680 0.000233 ***
## age         -0.01703    0.01560  -1.092 0.275013    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##     (Intr)
## age -0.903

Anova(glm1)

## Analysis of Deviance Table (Type II Wald chisquare tests)
## 
## Response: fec
##      Chisq Df Pr(>Chisq)
## age 1.1916  1      0.275

surdispersion_glm1 <- 1775/1325;surdispersion_glm1

## [1] 1.339623

AIC = 1775 et p-value = 0.27.



Pas de surdispersion observee.

3.2.1.2 Second

glm2 <- glmer(fec ~ year + (1| id),data=cham2, family = binomial)

## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
## Model failed to converge with max|grad| = 0.290051 (tol = 0.002, component 1)

## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, : Model is nearly unidentifiable: very large eigenvalue
##  - Rescale variables?;Model is nearly unidentifiable: large eigenvalue ratio
##  - Rescale variables?

summary(glm2)

## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: binomial  ( logit )
## Formula: fec ~ year + (1 | id)
##    Data: cham2
## 
##      AIC      BIC   logLik deviance df.resid 
##   1776.3   1791.8   -885.1   1770.3     1325 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -1.6666 -1.1423  0.6818  0.7912  1.0706 
## 
## Random effects:
##  Groups Name        Variance Std.Dev.
##  id     (Intercept) 0.2173   0.4662  
## Number of obs: 1328, groups:  id, 217
## 
## Fixed effects:
##               Estimate Std. Error z value Pr(>|z|)    
## (Intercept)  6.5452438  1.3195532   4.960 7.04e-07 ***
## year        -0.0030515  0.0006584  -4.634 3.58e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##      (Intr)
## year -0.999
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## Model failed to converge with max|grad| = 0.290051 (tol = 0.002, component 1)
## Model is nearly unidentifiable: very large eigenvalue
##  - Rescale variables?
## Model is nearly unidentifiable: large eigenvalue ratio
##  - Rescale variables?

3.2.1.3 Third

glm3 <- glmer(fec ~ age+ year + (1| id),data=cham2, family = binomial)

## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
## Model failed to converge with max|grad| = 0.292699 (tol = 0.002, component 1)

## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, : Model is nearly unidentifiable: very large eigenvalue
##  - Rescale variables?;Model is nearly unidentifiable: large eigenvalue ratio
##  - Rescale variables?

summary(glm3)

## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: binomial  ( logit )
## Formula: fec ~ age + year + (1 | id)
##    Data: cham2
## 
##      AIC      BIC   logLik deviance df.resid 
##   1777.1   1797.9   -884.6   1769.1     1324 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -1.6486 -1.1413  0.6819  0.7907  1.0438 
## 
## Random effects:
##  Groups Name        Variance Std.Dev.
##  id     (Intercept) 0.2128   0.4613  
## Number of obs: 1328, groups:  id, 217
## 
## Fixed effects:
##               Estimate Std. Error z value Pr(>|z|)  
## (Intercept)  2.8329285  1.3214401   2.144   0.0320 *
## age         -0.0167623  0.0155980  -1.075   0.2825  
## year        -0.0011244  0.0006564  -1.713   0.0867 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##      (Intr) age   
## age  -0.095       
## year -0.993 -0.013
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## Model failed to converge with max|grad| = 0.292699 (tol = 0.002, component 1)
## Model is nearly unidentifiable: very large eigenvalue
##  - Rescale variables?
## Model is nearly unidentifiable: large eigenvalue ratio
##  - Rescale variables?

3.2.1.4 Fourth

glm4 <- glmer(fec ~ age*year + (1| id),data=cham2, family = binomial)

## Warning: Some predictor variables are on very different scales: consider
## rescaling

## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
## Model failed to converge with max|grad| = 3.403 (tol = 0.002, component 1)

## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, : Model is nearly unidentifiable: very large eigenvalue
##  - Rescale variables?;Model is nearly unidentifiable: large eigenvalue ratio
##  - Rescale variables?

summary(glm4)

## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: binomial  ( logit )
## Formula: fec ~ age * year + (1 | id)
##    Data: cham2
## 
##      AIC      BIC   logLik deviance df.resid 
##   1779.1   1805.1   -884.6   1769.1     1323 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -1.6675 -1.1401  0.6837  0.7906  1.0334 
## 
## Random effects:
##  Groups Name        Variance Std.Dev.
##  id     (Intercept) 0.2095   0.4577  
## Number of obs: 1328, groups:  id, 217
## 
## Fixed effects:
##               Estimate Std. Error z value Pr(>|z|)    
## (Intercept)  1.082e+01  1.319e+00   8.207 2.26e-16 ***
## age         -8.721e-01  1.936e-02 -45.053  < 2e-16 ***
## year        -5.109e-03  6.551e-04  -7.799 6.23e-15 ***
## age:year     4.265e-04  8.441e-06  50.533  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##          (Intr) age    year  
## age      -0.073              
## year     -0.993 -0.002       
## age:year -0.007 -0.593 -0.014
## fit warnings:
## Some predictor variables are on very different scales: consider rescaling
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## Model failed to converge with max|grad| = 3.403 (tol = 0.002, component 1)
## Model is nearly unidentifiable: very large eigenvalue
##  - Rescale variables?
## Model is nearly unidentifiable: large eigenvalue ratio
##  - Rescale variables?

3.2.1.5 Fifth

glm5<- glmer(fec ~ age + (1| id) + (1| year),data=cham2, family = binomial)
summary(glm5)

## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: binomial  ( logit )
## Formula: fec ~ age + (1 | id) + (1 | year)
##    Data: cham2
## 
##      AIC      BIC   logLik deviance df.resid 
##   1750.5   1771.3   -871.2   1742.5     1324 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -1.9922 -1.0487  0.6251  0.7479  1.4398 
## 
## Random effects:
##  Groups Name        Variance Std.Dev.
##  id     (Intercept) 0.2402   0.4901  
##  year   (Intercept) 0.2214   0.4705  
## Number of obs: 1328, groups:  id, 217; year, 27
## 
## Fixed effects:
##             Estimate Std. Error z value Pr(>|z|)    
## (Intercept)  0.65014    0.18973   3.427 0.000611 ***
## age         -0.02212    0.01624  -1.362 0.173287    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##     (Intr)
## age -0.779

Anova(glm5)

## Analysis of Deviance Table (Type II Wald chisquare tests)
## 
## Response: fec
##      Chisq Df Pr(>Chisq)
## age 1.8543  1     0.1733

surdispersion_glm5 <- 1750/1324;surdispersion_glm5

## [1] 1.321752

AIC = 1750 et p-value = 0.17.



Pas de surdispersion observee.

4.2.1.1 First

glm6 <- glmer(fec ~ year + (1| id),data=cham2, family = binomial)

## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
## Model failed to converge with max|grad| = 0.290051 (tol = 0.002, component 1)

## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, : Model is nearly unidentifiable: very large eigenvalue
##  - Rescale variables?;Model is nearly unidentifiable: large eigenvalue ratio
##  - Rescale variables?

summary(glm6)

## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: binomial  ( logit )
## Formula: fec ~ year + (1 | id)
##    Data: cham2
## 
##      AIC      BIC   logLik deviance df.resid 
##   1776.3   1791.8   -885.1   1770.3     1325 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -1.6666 -1.1423  0.6818  0.7912  1.0706 
## 
## Random effects:
##  Groups Name        Variance Std.Dev.
##  id     (Intercept) 0.2173   0.4662  
## Number of obs: 1328, groups:  id, 217
## 
## Fixed effects:
##               Estimate Std. Error z value Pr(>|z|)    
## (Intercept)  6.5452438  1.3195532   4.960 7.04e-07 ***
## year        -0.0030515  0.0006584  -4.634 3.58e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##      (Intr)
## year -0.999
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## Model failed to converge with max|grad| = 0.290051 (tol = 0.002, component 1)
## Model is nearly unidentifiable: very large eigenvalue
##  - Rescale variables?
## Model is nearly unidentifiable: large eigenvalue ratio
##  - Rescale variables?

4.2.1.2 Second

Transformation de la variable year en variable normee reduite

year_scale<-scale(cham2$year, center=TRUE, scale= TRUE)

glm7 <- glmer(fec ~ year_scale + (1| id),data=cham2, family = binomial)
summary(glm7)

## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: binomial  ( logit )
## Formula: fec ~ year_scale + (1 | id)
##    Data: cham2
## 
##      AIC      BIC   logLik deviance df.resid 
##   1776.3   1791.8   -885.1   1770.3     1325 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -1.6666 -1.1423  0.6818  0.7912  1.0706 
## 
## Random effects:
##  Groups Name        Variance Std.Dev.
##  id     (Intercept) 0.2173   0.4662  
## Number of obs: 1328, groups:  id, 217
## 
## Fixed effects:
##             Estimate Std. Error z value Pr(>|z|)    
## (Intercept)  0.42505    0.06783   6.266  3.7e-10 ***
## year_scale  -0.01823    0.06530  -0.279     0.78    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##            (Intr)
## year_scale -0.001

surdispersion_glm7 <- 1776/1325;surdispersion_glm7

## [1] 1.340377

AIC = 1776 et p-value = 0.78.



Pas de surdispersion observee.

4.2.1.3 Third

glm8 <- glmer(fec ~ year_scale+age + (1| id),data=cham2, family = binomial)
summary(glm8)

## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: binomial  ( logit )
## Formula: fec ~ year_scale + age + (1 | id)
##    Data: cham2
## 
##      AIC      BIC   logLik deviance df.resid 
##   1777.1   1797.9   -884.6   1769.1     1324 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -1.6486 -1.1413  0.6819  0.7907  1.0438 
## 
## Random effects:
##  Groups Name        Variance Std.Dev.
##  id     (Intercept) 0.2128   0.4613  
## Number of obs: 1328, groups:  id, 217
## 
## Fixed effects:
##              Estimate Std. Error z value Pr(>|z|)    
## (Intercept)  0.577851   0.159379   3.626 0.000288 ***
## year_scale  -0.006749   0.066039  -0.102 0.918604    
## age         -0.016762   0.015809  -1.060 0.289001    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##            (Intr) yr_scl
## year_scale  0.146       
## age        -0.905 -0.163

surdispersion_glm8 <- 1777/1324;surdispersion_glm8

## [1] 1.342145

4.2.1.4 Fourth

glm9 <- glmer(fec ~ year_scale*age + (1| id),data=cham2, family = binomial)
summary(glm9)

## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: binomial  ( logit )
## Formula: fec ~ year_scale * age + (1 | id)
##    Data: cham2
## 
##      AIC      BIC   logLik deviance df.resid 
##   1779.1   1805.1   -884.6   1769.1     1323 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -1.6689 -1.1399  0.6839  0.7907  1.0327 
## 
## Random effects:
##  Groups Name        Variance Std.Dev.
##  id     (Intercept) 0.2092   0.4574  
## Number of obs: 1328, groups:  id, 217
## 
## Fixed effects:
##                 Estimate Std. Error z value Pr(>|z|)    
## (Intercept)     0.575862   0.159548   3.609 0.000307 ***
## year_scale     -0.032348   0.161967  -0.200 0.841699    
## age            -0.016602   0.015815  -1.050 0.293816    
## year_scale:age  0.002755   0.015923   0.173 0.862625    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) yr_scl age   
## year_scale   0.124              
## age         -0.906 -0.119       
## year_scal:g -0.072 -0.913  0.059

surdispersion_glm9 <- 1779/1323;surdispersion_glm9

## [1] 1.344671

5.2.1.1 First

lm1 <- lm(feconditetotale~long, data = cham_id)
summary(lm1)

## 
## Call:
## lm(formula = feconditetotale ~ long, data = cham_id)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -6.2342 -1.6839 -0.4381  1.6806  8.5451 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.38772    0.64837   0.598    0.551    
## long         0.25420    0.05203   4.886 2.47e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.715 on 161 degrees of freedom
## Multiple R-squared:  0.1291, Adjusted R-squared:  0.1237 
## F-statistic: 23.87 on 1 and 161 DF,  p-value: 2.468e-06

plot(lm1)

hist(resid(lm1))

lm2 <- lm(feconditetotale~log(long), data = cham_id)
summary(lm2)

## 
## Call:
## lm(formula = feconditetotale ~ log(long), data = cham_id)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -5.3527 -1.8484 -0.3931  1.6565  8.6115 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  -2.9773     1.2571  -2.368    0.019 *  
## log(long)     2.6567     0.5178   5.131 8.22e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.697 on 161 degrees of freedom
## Multiple R-squared:  0.1405, Adjusted R-squared:  0.1352 
## F-statistic: 26.32 on 1 and 161 DF,  p-value: 8.223e-07

plot(lm2)

lm2bis <- lm(sqrt(feconditetotale)~long, data = cham_id)
summary(lm2bis)

## 
## Call:
## lm(formula = sqrt(feconditetotale) ~ long, data = cham_id)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -2.34105 -0.45584  0.02148  0.60739  1.70711 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.88677    0.19418   4.567 9.79e-06 ***
## long         0.06323    0.01558   4.058 7.70e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.813 on 161 degrees of freedom
## Multiple R-squared:  0.09279,    Adjusted R-squared:  0.08716 
## F-statistic: 16.47 on 1 and 161 DF,  p-value: 7.699e-05

plot(lm2bis)

cham_id2 <- cham_id[cham_id$feconditetotale!=0,]
lm3 <- lm(log(feconditetotale)~(log(long)), data = cham_id2)
summary(lm3)

## 
## Call:
## lm(formula = log(feconditetotale) ~ (log(long)), data = cham_id2)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.47197 -0.49128  0.05571  0.57801  1.44308 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  -1.0820     0.3588  -3.015  0.00303 ** 
## log(long)     0.8836     0.1476   5.988  1.6e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6917 on 145 degrees of freedom
## Multiple R-squared:  0.1983, Adjusted R-squared:  0.1927 
## F-statistic: 35.86 on 1 and 145 DF,  p-value: 1.596e-08

plot(lm3)

lm4 <- lm(log(feconditetotale+1)~(long), data = cham_id2)
summary(lm4)

## 
## Call:
## lm(formula = log(feconditetotale + 1) ~ (long), data = cham_id2)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.09994 -0.33845 -0.02604  0.41327  1.17593 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.65085    0.13462   4.835 3.36e-06 ***
## long         0.06346    0.01087   5.839 3.32e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5062 on 145 degrees of freedom
## Multiple R-squared:  0.1903, Adjusted R-squared:  0.1848 
## F-statistic: 34.09 on 1 and 145 DF,  p-value: 3.316e-08

plot(lm4)

lm6 <- lm(fecrelative~long, data = cham_id)
summary(lm6)

## 
## Call:
## lm(formula = fecrelative ~ long, data = cham_id)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.57254 -0.23862 -0.00058  0.21381  0.85628 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  5.727e-01  7.239e-02   7.911 3.87e-13 ***
## long        -4.066e-05  5.809e-03  -0.007    0.994    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3031 on 161 degrees of freedom
## Multiple R-squared:  3.044e-07,  Adjusted R-squared:  -0.006211 
## F-statistic: 4.9e-05 on 1 and 161 DF,  p-value: 0.9944

plot(lm6)

lm6 <- lm(log(fecrelative)~long, data = cham_id2)
summary(lm6)

## 
## Call:
## lm(formula = log(fecrelative) ~ long, data = cham_id2)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.53235 -0.29253  0.06901  0.30220  0.90812 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -0.59059    0.11470  -5.149 8.38e-07 ***
## long         0.00435    0.00926   0.470    0.639    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4313 on 145 degrees of freedom
## Multiple R-squared:  0.001519,   Adjusted R-squared:  -0.005367 
## F-statistic: 0.2207 on 1 and 145 DF,  p-value: 0.6392

plot(lm6)

glm9 <- glm(data=cham_id, feconditetotale~long, family="poisson")
summary(glm9)

## 
## Call:
## glm(formula = feconditetotale ~ long, family = "poisson", data = cham_id)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -3.8642  -1.1470  -0.4008   0.8318   3.4669  
## 
## Coefficients:
##             Estimate Std. Error z value Pr(>|z|)    
## (Intercept)  0.29098    0.14186   2.051   0.0402 *  
## long         0.07476    0.01039   7.198 6.09e-13 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for poisson family taken to be 1)
## 
##     Null deviance: 397.41  on 162  degrees of freedom
## Residual deviance: 345.61  on 161  degrees of freedom
## AIC: 783.81
## 
## Number of Fisher Scoring iterations: 5

glm10 <- glm(data=cham_id, feconditetotale~long, family="quasipoisson")
summary(glm10)

## 
## Call:
## glm(formula = feconditetotale ~ long, family = "quasipoisson", 
##     data = cham_id)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -3.8642  -1.1470  -0.4008   0.8318   3.4669  
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.29098    0.20088   1.449    0.149    
## long         0.07476    0.01471   5.083 1.02e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for quasipoisson family taken to be 2.005336)
## 
##     Null deviance: 397.41  on 162  degrees of freedom
## Residual deviance: 345.61  on 161  degrees of freedom
## AIC: NA
## 
## Number of Fisher Scoring iterations: 5

6.2.1.1 First

glm11 <- glmer(fec ~ long + (1| id),data=cham2, family = binomial)
summary(glm11)

## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: binomial  ( logit )
## Formula: fec ~ long + (1 | id)
##    Data: cham2
## 
##      AIC      BIC   logLik deviance df.resid 
##   1231.2   1245.6   -612.6   1225.2      917 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -1.7987 -1.0648  0.6503  0.7841  1.2074 
## 
## Random effects:
##  Groups Name        Variance Std.Dev.
##  id     (Intercept) 0.3248   0.5699  
## Number of obs: 920, groups:  id, 163
## 
## Fixed effects:
##             Estimate Std. Error z value Pr(>|z|)
## (Intercept)  0.23862    0.29226   0.816    0.414
## long         0.01167    0.02217   0.526    0.599
## 
## Correlation of Fixed Effects:
##      (Intr)
## long -0.955

Anova(glm11)

## Analysis of Deviance Table (Type II Wald chisquare tests)
## 
## Response: fec
##       Chisq Df Pr(>Chisq)
## long 0.2771  1     0.5986